Feedback Amplifiers: Complete Beginner's Guide For students.

A feedback amplifier feeds a fraction of its output back to the input. When the fed-back signal subtracts, the feedback is negative, and the amplifier becomes far more stable, linear and predictable than its raw transistors could ever be alone. Nearly every op-amp circuit is a feedback amplifier.

Bare transistors are unruly: gain drifts with temperature and varies device to device. Negative feedback trades excess raw gain for precision, wider bandwidth and lower distortion, which is why a cheap op-amp holds gain to a fraction of a percent while its insides drift.

Key Concepts

• Feedback factor (beta): Fraction fed back, beta = Vf/Vout, often set by a resistive divider.
• Loop gain: A x beta. Large loop gain means strong feedback and all its benefits.
• Closed-loop gain: Af = A/(1 + A x beta), approximately 1/beta when loop gain is large, set by the feedback network, not the amplifier.
• Desensitivity: Internal gain drift is divided by (1 + A x beta) at the output.
• Bandwidth extension: Negative feedback stretches bandwidth by (1 + A x beta).
• Distortion/noise: Harmonics generated inside the loop shrink by (1 + A x beta); noise after the feedback tap is not reduced.
• Four topologies: Voltage-series (non-inverting amp: input R up, output R down), voltage-shunt (inverting: both down), current-series (both up), current-shunt (input down, output up).
• Positive feedback: Feeds back in phase; at loop gain exactly 1 with zero phase shift the circuit oscillates (Barkhausen), also the basis of the Schmitt trigger.

Formulas

• Closed-loop gain: Af = A/(1 + A x beta).
• Stability: dAf/Af = (dA/A)/(1 + A x beta).
• Bandwidth: f(Hf) = f(H) x (1 + A x beta); lower cutoff divided by the same factor.
• Limits: Assumes one loop and frequency-independent beta. At high frequencies, phase shift can flip negative feedback positive, causing oscillation, so stability margins must be checked.

Worked Example

Open-loop gain A = 10,000; want Af = 100. Step 1: beta = (A/Af - 1)/A = 99/10,000 = 0.0099. Step 2: nominal Af = 10,000/100 = 100. Step 3: A drifts 20 percent down to 8,000: Af = 8,000/(1 + 79.2) = 99.75. Step 4: A drifts up to 12,000: Af = 12,000/119.8 = 100.17. A ±20 percent internal swing becomes ±0.25 percent outside: the magic of feedback in one calculation.

Common Misconceptions

• "Feedback wastes gain." The sacrificed gain buys stability, bandwidth and linearity no open-loop design can match.
• "It removes all distortion." It divides distortion by (1 + A x beta), dramatic but not infinite, and only inside the loop.
• "More feedback is always safer." With high-frequency phase shift, excess feedback turns negative into positive and the amplifier oscillates.

Real-World Applications

• Audio: Feedback holds hi-fi distortion to tiny fractions of a percent.
• Op-amp circuits: Every inverting/non-inverting/summing amp is a feedback amplifier.
• Regulators: Linear regulators compare divided output to a reference and correct the pass transistor.
• Followers: A common-collector stage is 100-percent voltage-series feedback, hence gain ~1 and low output impedance.

Negative feedback samples the output, subtracts it at the input, and continuously corrects the error: Af = A/(1 + A x beta), about 1/beta for large loop gain. The example proves the payoff, ±20 percent raw drift collapses to ±0.25 percent. Bandwidth stretches, distortion shrinks, resistances follow the chosen topology. Just watch high-frequency phase: feedback with the wrong phase becomes an oscillator.